Mexican province, briefly an independent nation and now a U.S. state, from Spanish Texas, Tejas, earlier pronounced "ta-shas," originally an ethnic name, from Caddo (eastern Texas Indian tribe) taysha "friends, allies," written by the Spanish as a plural. Related: Texan. The alternative form Texian is attested from 1835 and was the prevailing form in U.S. newspapers before 1844.
The baseball Texas-leaguer "ball popped up just over the head of the infielders and falling too close for outfielders to catch" is recorded from 1905, named for the minor league that operated in Texas from 1902 (one theory is that outfielders played unusually deep in Texas because hit balls bounced hard off the hard, sun-baked ground).
<a href="https://www.etymonline.com/word/tejano">Etymology of tejano by etymonline</a>
Harper, D. (n.d.). Etymology of tejano. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/tejano